The analytical characterization of coverage probability in finite three-dimensional wireless networks has long remained an open problem, hindered by the loss of spatial independence in finite-node settings and the coupling between link distances and interference in bounded geometries. This paper closes this gap by presenting the first exact analytical framework for coverage probability in finite 3D networks modeled by a binomial point process within a cylindrical region. To bypass the intractability that has long hindered such analyses, we leverage the independence structure, convolution geometry, and derivative properties of Laplace transforms, yielding a formulation that is both mathematically exact and computationally efficient. Extensive Monte Carlo simulations verify the analysis and demonstrate significant accuracy gains over conventional Poisson-based models. The results generalize to any confined 3D wireless system, including aerial, underwater, and robotic networks.

翻译：有限三维无线网络覆盖概率的解析表征长期以来一直是一个悬而未决的问题，其难点在于有限节点设置中空间独立性的丧失，以及有界几何结构中链路距离与干扰之间的耦合。本文通过提出首个针对圆柱区域内二项点过程建模的有限三维网络覆盖概率精确解析框架，填补了这一空白。为规避长期阻碍此类分析的复杂性，我们利用拉普拉斯变换的独立性结构、卷积几何与导数特性，推导出兼具数学精确性与计算高效性的表达式。大量蒙特卡洛仿真验证了该分析，并证明其相较于传统泊松模型具有显著的精度提升。该结果可推广至任何受限三维无线系统，包括空中、水下及机器人网络。